Poetry

Democritus’s Cone

by Sarah Adams

A paradox, one less well-known, Asks us to contemplate a cone: A figure with smooth sloping sides Which horizontally divides Into two halves, so that have we Two surfaces: one a, one b. The bottom of the top we’ll say Is denoted by the letter a, And b denotes the upper side Of the half which did reside Directly underneath the top Antecedent to the chop.

So let us turn now and reflect Upon the cone we did bisect. Something will be shown amiss When we now consider this: Is the area of b the same As that of a (the surface plane at the bottom of the top, we said), Or is unequal b instead? Either answer can’t be true, The reasons I will talk you through: If a unequal is to b Then after all cannot have we A cone with edges smoothly sloping (This is surely thought-provoking) But a pyramid: something stepped. This you will have to accept, For surfaces different in size Lead us to the cone’s demise. And yet if b to a is equal To the cone this too proves lethal, For once we’ve chosen to profess That indeed we do possess Surfaces stacked up high,The same in size (not just nearby) Then somewhat paradoxically, The cone is not a cone, you see, But a cylinder.

This site uses cookies to recognize users and allow us to analyse site usage. By continuing to browse the site with cookies enabled in your browser, you consent to the use of cookies in accordance with our privacy policy. X